Monoand bi-disperse rectangular cuboidal granules are assembled from colloid-hydrogel suspensions via stop-flow lithography and fully submerged in hexadecane. Their packing density and structural evolution are studied as a function of agitation time using micro-computed X-ray tomography. When subjected to periodic agitation, the granule packing density increases logarithmically in time; concomi...

We consider the problem of constructing dense lattices of Rn with a given non trivial automorphism group. We exhibit a family of such lattices of density at least cn2−n, which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions n, we exhibit a finite set of lattices that come with an automorphism group of size n, and a co...

We consider the variational problem of maximizing the packing density on some finite dimensional set of almost periodic sphere packings. We show that the maximal density on this manifold is obtained by periodic packings. Since the density is a continuous, but a nondifferentiable function on this manifold, the variational problem is related to number theoretical questions. Every sphere packing i...

This paper formalizes the local density inequality approach to getting upper bounds for sphere packing densities in Rn. This approach was first suggested by L. Fejes-Tóth in 1954 as a method to prove the Kepler conjecture that the densest packing of unit spheres in R has density π √ 18 , which is attained by the “cannonball packing.” Local density inequalities give upper bounds for the sphere p...

The notion of a completely saturated packing [1] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent dense packings and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, ...

The densest amorphous packing of rigid particles is known as random close packing. It has long been appreciated that higher densities are achieved by using collections of particles with a variety of sizes. For spheres, the variety of sizes is often quantified by the polydispersity of the particle size distribution: the standard deviation of the radius divided by the mean radius. Several prior s...

A coding error was found in calculating the optimal packing distribution of our geodesic array. The error was corrected and the new optimization results in slightly improved packing density. The overall approach and algorithm remain unchanged.